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Fig. 12.1. Surface temperature fluctuations with periods and amplitudes (after V.A. Kudryavtsev): I - Tl = 10 years, At = 0.5°C; II - T2 = 40 years, A2 = 1 °C; III -T3 = 300 years, A} = 2°C; IV - resulting curve at their superposition.

In the upper layers of the lithosphere a multitude of periodic temperature fluctuations of various periods and amplitudes from daily and yearly to many years are observed: rperi = 11 years; Tperi = 40 years; Tper3 = 300 years;...; Tper = 1800 years and others with periods of ten and a hundred years. Some of these fluctuations may, it seems, have causes of an astronomical nature, others arise by periodic changes of the geological environment and geographical situation in the course of the Earth's evolution. Thus, for example, it is shown in the work by M. Milankovich Mathematical theory of climatic fluctuations that if we use the periodic precessional change of the position of the Earth's rotational axis and periodic change of its mean albedo value taking place in this case, as one of the reasons for this process, we can discern four minima corresponding to four glaciations in the Northern Hemisphere and three relative maxima between them representing interglacials and the thermal maximum after glaciation in the Quaternary period on the background of one general wave of cooling of period Tper = n x 100 000 years. At the present time the majority of researchers assume the existence of many years' fluctuations of heat exchange conditions on the lithosphere surface with relatively short period (up to a few hundred years), medium (from a few hundred to a few thousand years) and long period (from a few thousand years to a hundred thousand years) as a whole.

As these fluctuations propagate downward through the ground, the damping out (reduction) of the amplitude Aper with depth is observed as it is known from Fourier's first law (see §1.1) and phase delay (in time) of the ground temperature fluctuation takes place as is known from Fourier's second law. The shorter the period of the temperature fluctuation Tper the sharper is the damping of the amplitude, i.e. according to Fourier's third law the fluctuations extend for a smaller depth. This phenomenon is rather well illustrated in Fig. 12.2. Actually, in layer / four temperature fluctuations, the seasonal (one per year) and the subsequent three periods are superimposed. In layer II the yearly fluctuations are not traced while the 10-, 40- and 300-year fluctuations are superimposed. In layer III only 40- and 300-year temperature fluctuations exist. In layer I V there is only the temperature fluctuations of the longest period Tper = 300 years. At one and the same depth both the rise and the fall of temperature (see Fig. 12.2, curve 4) associated with penetration of either the warm or the cold portion of the integrated temperature wave to this depth can be observed at different moments of time. In other words, degradational and aggradational trends in the development of the permafrost can exist simultaneously at various depths in one and the same place. Such analysis allowed Kudryavtsev to show that such fluctuations can substantially violate, for example, the general rule of the permafrost thickness increasing from the south northward (Fig. 12.3). Suppose that the fluctuations of the period T£er = 10 years cause permafrost degradation, while the fluctuations of the period Tper = 40 years and = 300 years lead to aggradation and degradation respectively, with the effect of 40-year fluctuations being stronger than that of 300-year ones. Based on this fact the degradational trend causing reduction of permafrost thickness will dominate in the first layer as a result of the superimposing of temperature fluctuations of different periods and phases (two degradational effects and one aggradational effect). In the second layer fluctuations of T£er = 10 years do not occur while the 40-year (aggradational) and 300-year (degradational) ones lead to the aggradation process dominating, i.e. there is increase of permafrost thickness. The fluctuation with the 300-year period provides the degradational trend in the permafrost (decrease of its thickness) and is the only one penetrating into the last (third) layer. Ultimately, instead of the conventionally linear increase of the permafrost thickness from the south northward presented in Fig. 12.3 as a line AB there is a rather characteristic curve of the change in permafrost thickness south northward (shown as a broken line). It follows from Fig. 12.3 that in different places we can find alternation of the processes of degradation and aggradation when moving from south northward.

It is necessary to view the processes of permafrost aggradation and

Fig. 12.2. Attenuation of amplitudes with depths depending on the period of the temperature fluctuations: 1 - T1 = 10 years; 2 - T2 = 40 years; 3 -T3 = 300 years; 4 - integrated rock temperature; a,b,c- envelopes of temperature fluctuations with various periods.

degradation for the specific places and depths and to associate them with the specific time intervals and periods of fluctuations. Thus, as is shown by Kudryavtsev, permafrost development is a result of the continuous process of superimposition of a great number of temperature fluctuations with various periods and amplitudes on the Earth's surface and their propagation into the ground depending on the whole combination of geological and geographical factors and conditions.

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